The 84-year-old entertainer told jurors at Southwark Crown Court that he was left feeling "sickened" by his behaviour, blaming himself for the alcohol problem the woman developed.
But he insisted that their affair was "consensual" and she was a "willing participant" in the string of sexual encounters they had.
Harris faces 12 counts of indecent assault on four alleged victims between 1968 and 1986, all of which he denies.
Giving evidence at the start of his defence, the artist rebuffed all the allegations, including claims from his daughter's friend - which relate to seven counts - but admitted they had had several intimate encounters beginning when she was around 18.
He revealed that he had a second affair with a woman that he and wife Alwen allowed to live rent-free in an annexe at their home.
When questioned about the allegations relating to his daughter Bindi's friend - which the alleged victim claims date back to when they were on holiday in Hawaii when she was 13 - the TV personality said their relationship only began when she was an adult. Harris told the court: "It was all consensual and everything that had happened, she had been a willing participant."
But the 84-year-old told the court: "I felt that I had betrayed everybody... Betrayed their trust."
Pressed by his defence barrister Sonia Woodley QC on why he felt such remorse, Harris's voice broke as he told jurors: "Because I'd had an affair with their daughter who was much younger than me. An extra-marital affair."
Harris said he felt "sickened by myself for being a part of it at all", adding: "I knew it was wrong. Here I was, much older than her."
He said he originally told police there had only been two sexual encounters with the girl as he felt "huge embarrassment".
Harris said that the pair's first intimate encounter happened when she was 18 as he took her a cup of tea in bed when she stayed at his home in Bray, Berkshire.
He described how she appeared to "invite" him to touch her, behaving in a "flirtatious" way. "I put the tea down on the bedside table and she grabbed my elbow and seemed to indicate that she wanted me to sit on the bed, which I did.
"She slid over a little bit and then shook the duvet off her foot to reveal that her legs were bare, she had no pyjama pants on.
"And it seemed to me that she was being very flirtatious with me. As you can imagine, it was a very flattering feeling for this young lady to suddenly be showing an interest in me."
Harris, who earlier admitted he was a "touchy-feely" person, described how his "heart was thumping" as he touched the girl's leg, before leaving the room."
He added: "It seemed to be an invitation, shaking off the duvet."
The encounter started a series of sexual encounters between the pair, Harris said, in all of which he claimed she was a willing participant, and instigated some.
Later, after receiving several "unintelligible phone messages" from the woman, Harris visited her.
He said: "She was blaming me for the state she was in, destroying her life, she said," he told the court.
"I said 'please forgive me', and she said, 'I forgive you'."
The woman asked for £25,000 so she could open an animal sanctuary, he said, and when he refused she became "irate", beating him with clenched fists, and told him: "You'd better keep your eye on the weekend papers".
He said: "I kept waiting for each weekend to have some newspaper article destroying me."
The court also heard that Harris embarked on a second affair with a woman he and his wife allowed to stay in a separate annexe they built for their daughter around 1995/96.
He said they allowed the woman, who was "down on her luck", to stay in the house rent-free, but a relationship developed.
"It gradually became physical," he told the court.
The trial, at Southwark Crown Court, will continue today.